Related papers: Stochastic Models of Evolution in Genetics, Ecolog…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology, i.e. in cancer evolution. These dynamics play an important…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Social networks exhibit strikingly systematic patterns across a wide range of human contexts. While genetic variation accounts for a significant portion of the variation in many complex social behaviors, the heritability of egocentric…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
The Semantic Theory of Evolution (STE) takes the existence of a number of arbitrary communication codes as a fundamental feature of life, from the genetic code to human cultural communication codes. Their arbitrariness enables, at each…
Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm…
This talk will review a little over a decade's research on applying certain stochastic models to biological sequence analysis. The models themselves have a longer history, going back over 30 years, although many novel variants have arisen…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…